The article: “Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation” by Marc P. C. Fossorier published in IEEE Transactions on Communications, vol. 47, No. 5, May 1999, [1] describes an iterative algorithm for decoding LDPC codes. LDPC codes are error-correcting codes of which the decoders can accept soft decision inputs. LDPC decoding does not involve Viterbi-kind of algorithms and is much less complex. LDPC codes were invented in the 1960s by Gallager. Later in the 1990s, Berrou et al. invented Turbo codes. Then, MacKay and others discovered that Turbo codes were similar to LDPC codes.
In the sequel, the abbreviation LDPC will be used to designate all codes with a Low-Density Parity Check matrix, including Turbo codes.